Attribute selection methods based on graph theory in updated formal contexts

Two types of attribute filtering methods for granular reduct of updated formal contexts are considered based on graph theory. In the first type of attribute filtering method, a covering matrix is defined for each attribute. The elements in this matrix are either 0 or 1 according to whether the attribute belongs to the granular discernibility set between two objects. It is proven that the sum of elements in the covering matrix is equal to the degree of the corresponding attribute. This precisely reflects the discernibility of this attribute. A DGRS algorithm for calculating the granular reduct is proposed based on the above principle. Subsequently, the changes in attribute degree are demonstrated when attributes or objects are added, meanwhile, the relationship between the granular reduct of the updated formal context and the original granular reduct is verified. Finally, the ODGRS and ADGRS algorithms are provided to filter out new granular reduct based on the original granular reduct when objects or attributes are added. In the second type of attribute filtering method, the columns corresponding to the attributes in the formal context are employed to study the attributes. The definition of edge label of attribute is provided, and it is verified that the degree of an attribute is equal to the number of elements in the edge label of the attribute. Subsequently, it is determined that the intersection of edge labels can be employed to ascertain whether two attributes are connected. Furthermore, the difference operation of edge labels can be utilized to remove the edges connected to the attribute with the highest degree. Finally, the DGRS, ODGRS and ADGRS algorithms are updated, and the effectiveness of the updated algorithms is verified through experiments.